As a numerical calculation method of calculating the motion of a continuum, such as a fluid or an elastic body a finite difference method, a finite element method, or a finite volume method has been used which finds the approximate solution of a differential equation based on a numerical mesh. In addition, in recent years, since numerical calculation has been used in the field of application such as computer aided engineering (CAE), the numerical calculation method of calculating the state of the continuum has been developed and the problem of the interaction between a fluid and a structure has been solved. However, in the numerical calculation method using the numerical mesh, when a moving boundary problem, such as the existence of an interface including a free surface or a problem in fluid-structure interaction analysis for analyzing the interaction between a fluid and a structure, occurs, it is difficult to treat the continuum. Therefore, in some cases, it is difficult to create a program.
As the numerical calculation method without using the numerical mesh, there is a particle method. The particle method analyzes the motion of a continuum as the motion of a finite number of particles. A representative particle method which is currently proposed is, for example, a smoothed particle hydrodynamics (SPH) method or a moving particle semi-implicit (MPS) method. The particle method can analyze the motion of the continuum without a special measure in the treatment of the moving boundary. Therefore, in recent years, the particle method has been widely used as the numerical calculation method of calculating the motion of the continuum.
In the field of structure analysis, in some cases, the contact between objects, such as the collision between objects, is calculated. Software based on the finite element method, such as LS-DYNA (registered trademark), treats the contact problem from the geometrical shape of a numerical mesh. However, the particle method does not generate the numerical mesh. Therefore, in the calculation of the contact, when another particle enters a sphere with a predetermined radius hs from a particle, the particle method performs the calculation such that reaction force is applied to the particles. FIG. 8 is a diagram illustrating an example of the reaction force calculated by the conventional particle method. In the example illustrated in FIG. 8, a particle 91 is arranged in the radius hs of a particle 90. In the example illustrated in FIG. 8, the particle 90 is arranged in the radius hs of the particle 91. In the example illustrated in FIG. 8, the particle method calculates reaction force 90a applied from the particle 90 to the particle 91. In addition, the particle method calculates reaction force 91a applied from the particle 91 to the particle 90.
The particle method uses the following Equation (1) as a potential function applied to, for example, particles i and j.
                                          φ            ij                    ⁡                      (                                                                          x                  i                                -                                  x                  j                                                                    )                          =                  {                                                                      c                  ⁢                                                                          ⁢                                      log                    ⁡                                          (                                                                                                                                                            x                              i                                                        -                                                          x                              j                                                                                                                                                          h                          s                                                                    )                                                                                                                                                                                                          x                        i                                            -                                              x                        j                                                                                                  <                                      h                    s                                                                                                      0                                                                                                                                                    x                        i                                            -                                              x                        j                                                                                                  ≥                                      h                    s                                                                                                          (        1        )            
Herein, xi and xj are the position vectors of the particle i and the particle j, respectively. In addition, c is a constant.
The reaction force applied from the particle j to the particle i by the potential represented by Equation (1) is obtained as
                    -                              ∂                          φ              ij                                            ∂                          x              i                                                          (                  Expression          ⁢                                          ⁢          2                )            and the reaction force applied from the particle i to the particle j by the potential is obtained as
                    -                                            ∂                              φ                ij                                                    ∂                              x                j                                              .                                    (                  Expression          ⁢                                          ⁢          3                )            
Another example of the particle method of calculating the contact is a method which calculates a contact point of a closed surface other than the sphere when the contact point of the particle is calculated.
With regard to the conventional technologies, refer to Japanese Laid-open Patent Publication No. 2009-26279, for example.
However, the conventional particle method represents the potential region in a spherical shape. Therefore, in the conventional particle method, when the contact problem between deformable bodies, such as elastic bodies, is treated, in some cases, the particle after deformation can infiltrate into the region, into which the particle could not infiltrate before deformation. In this case, since the calculation region of a given particle includes another particle, the accuracy of calculating reaction force is deteriorated in the conventional particle method. FIGS. 9 and 10 are diagrams illustrating an example of the problems of the conventional particle method. FIG. 9 illustrates an example of the arrangement of particles 80 of an elastic body before deformation at the beginning of the simulation by the conventional particle method. As illustrated in the example of FIG. 9, two particles 80 are arranged such that the regions thereof within radius hs overlap each other. Therefore, it is difficult for a particle 81 of an elastic body different from the elastic body including the particle 80 to infiltrate between the two particles 80.
FIG. 10 illustrates an example of the arrangement of the particles 80 of the elastic body after deformation in the middle of the simulation by the conventional particle method. As illustrated in the example of FIG. 10, two particles 80 are deformed in such a direction that they are kept separated from each other and that the regions thereof within the radius hs do not overlap each other. Therefore, a particle 81 of an elastic body different from the elastic body including the particle 80 can infiltrate between the two particles 80. When the particle 81 infiltrates between the two particles 80, the particle 80 is arranged on the calculation region of the particle 81 and the particle 81 is arranged on the calculation region of the particle 80. Therefore, in the example illustrated in FIG. 10, the accuracy of calculating reaction force is deteriorated.